propositional logic

Description

Propositional logic is a sub-branch of symbolic logic studying the truth values of propositional formulas.

• a proposition is a statement that can be either true or false, but not both (i.e. having a truth value)
• an atomic proposition has a truth value (truth or falsity) not dependent upon the truth value of any other proposition
  • may abbreviate as propositional variable, e.g. $p,q,r...$
• connectives allow building up complex propositions
  • $\land$, And, conjunction, e.g. $p \land q$
  • $\lor$, Or, disjunction, e.g. $p \lor q$
  • $\implies$, If... Then..., conditional or implication, e.g. $p \implies q$
  • $\iff$, Iff, biconditional, e.g. $p \iff q$
    • "if and only if"
  • $\lnot$, Not, negation, e.g. $\lnot p$
  • $(\quad)$, Comments, disambiguation, e.g. $(p \land (q \implies r)) \lor s$
    • parentheses

Notes

• various systems for determining truth values of propositional formulas, such as natural deduction and method of truth tables

See also

• predicate
• Boolean satisfiability problem
• truth table
• compare syllogistic logic (introduced by Aristotle in Posterior Analytics)

References

1. https://proofwiki.org/wiki/Definition:Propositional_Logic
2. https://ncatlab.org/nlab/show/propositional+logic
3. https://plato.stanford.edu/entries/logic-propositional/
4. http://intrologic.stanford.edu/chapters/chapter_02.html
5. https://www.cs.ox.ac.uk/people/michael.wooldridge/teaching/soft-eng/lect07.pdf